Why are the third generation superpartners lighter than the other sfermions in mSUGRA?

Question

In the mSUGRA (minimal supergravity) breaking scenario, the stop particle typically appears at energies reachable at the LHC. Other sfermions, notably the partners of up, down, strange and charm are assumed to be degenerate in mass, and also heavier than the stop. Something similar holds for the stau.

Why is the third generation different in mSUGRA (not degenerate as the first two), and why is the mass hierarchy inverted wrt. the Standard Model sector (3rd generation sparticles lighter)?

(I guess these features are not neccessarily specific to mSUGRA, but might apply to more general models as well.)

Answer 1

In short, the answer goes like this: All fermion masses are assumed to unify at some high scale (e.g.~$10^{16} GeV$) in MSUGRA. So, the mass differences between them at low energies are due to the running of the masses from that high scale down to the observed scale (e.g. ~1TeV at the LHC). The $\beta$ function for the stop mass has a positive contribution due to the top Yukawa coupling,$y_t$, which is large due to the fact that the top mass is not small compared to the Higgs vacuum expectation value,$v$, ($m_t = y_tv$). This implies that the stop mass drops more rapidly as the renormalization scale is lowered than the 1st and 2nd generation squarks, which have negligible Yukawa couplings. This leads to a mass spectrum where the stop is light and the first two generation squarks are nearly degenerate (ditto for the stau).

The Supersymmetry Primer by Martin has a good discussion of this (http://arxiv.org/abs/hep-ph/9709356), particularly on pg. 46 (where you can find the $\beta$ functions) and 75 (which discusses the squark and slepton spectrum).